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master's thesis
Varijacijske nejednakosti
Zagreb: University of Zagreb, Faculty of Science, 2016. urn:nbn:hr:217:804787
Pjanić, Matea
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Pjanić, M. (2016). Varijacijske nejednakosti (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:804787

Pjanić, Matea. "Varijacijske nejednakosti." Master's thesis, University of Zagreb, Faculty of Science, 2016. https://urn.nsk.hr/urn:nbn:hr:217:804787

Pjanić, Matea. "Varijacijske nejednakosti." Master's thesis, University of Zagreb, Faculty of Science, 2016. https://urn.nsk.hr/urn:nbn:hr:217:804787

Pjanić, M. (2016). 'Varijacijske nejednakosti', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:804787

Pjanić M. Varijacijske nejednakosti [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2016 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:804787

M. Pjanić, "Varijacijske nejednakosti", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2016. Available at: https://urn.nsk.hr/urn:nbn:hr:217:804787

Metadata
TitleVarijacijske nejednakosti
AuthorMatea Pjanić
MentorZvonimir Tutek (mentor)
Committee memberZvonimir Tutek (predsjednik povjerenstva)
Committee memberMarko Vrdoljak (član povjerenstva)
Committee memberLuka Grubišić (član povjerenstva)
Committee memberVedran Čačić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2016-07-14, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu proučavamo jednofazni Stefanov problem, rubni problem sa slobodnom granicom koja se pomiče uslijed djelovanja topline. Stefanov problem prikazali smo kao proces otapljanja leda; matematički, kao jednadžbu provođenja s rubnim i inicijalnim uvjetom, te uvjetom na nepoznatoj pomičnoj granici između vode i leda. Zbog svojstva monotonosti invertibilnosti funkcije pomičnog ruba, Stefanov problem možemo prikazali u obliku paraboličke varijacijske nejednakosti za koje smo pokazali egzistenciju i jedinstvenost rješenja u Sobolevljevom prostoru, koji je također detaljno objašnjen. Na kraju smo formirali diskretno rješenje pomoću metode konačnih elemenata, te dali rezultate stabilnosti i konvergencije za numerička rješenja problema.
Abstract (english)
In this thesis we analyze one-phase Stefan problem, boundary problem with moving barrier, which is moving due to heat transfer. Stefan problem is process of a melting of ice; and mathematically, it is heat equation with initial and boundary condition, and condition on unknown barrier between water and ice. Due to monotonicity and invertibility of the moving barrier function, we could transform Stefan problem in parabolic variational inequality, for which we showed uniqueness and existence of solution in Sobolev space, which is also explained in detail. In the end we form discrete solution by means of finite element approximation, and give some results on stability and convergence for numerical solutions.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:804787
Study programmeTitle: Applied Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-01-30 09:45:05